A group of Government and opposition TDs hope to use the Constitution to bring the proposed abortion legislation to a referendum.
Under Article 27, the President can refuse to sign the Bill - if he is petitioned by at least 55 TDs and 30 Senators.
Members of Fine Gael, Labour and a number of Independents have held meetings in recent weeks to try to win enough support for the vote.
Among the deputies taking part is former Labour Party Chairman Colm Keaveney.
He says the group wants the people to have a say in the legislation and that it's passing should not be left to the party whip system.